python实现 BLEU 评价方法n-gram 加权平均

这里用的是几何加权平均数

我们生活中常用的算术加权平均数是
$$\frac{w_0{x}_0+w_1{x}_1..}{w_0+w_1..}$$
而几何加权平均数是
$$\sqrt[(\sum w)]{\prod wx}$$
那我们在这个基础上演变一下
$$\begin{gathered} \sqrt[(\sum w)]{\prod x^w} \\ =e^{ln(\sqrt[(\sum w)]{\prod x^w})} \\ =e^{\frac{ln(\prod x^w)}{\sum w}} \\ =e^{\frac{\sum wlnx}{\sum w}} \end{gathered}$$
一般资料上的n-gram加权平均没有分母，还有为什么要表现成这个形式

，不写成${\sum }_{i=1}^N{P}_n^{w_n}$这种形式，应该是为了简化运算吧，这种形式要做好多次乘方和加法

from collections import Counter
from math import  exp
import nltk

def bleuMultiGram(candidate,reference,maxn,weight):
    sum=0
    if(weight):
        for i in range (1,maxn+1):
            sum+=exp(weight[i-1]*bleu(candidate,reference,i))
    else:
        for i in range(1, maxn + 1):
            sum += exp(bleu(candidate, reference, i)) #默认权重都为1
    if(len(ngram(candidate,1))>len(ngram(reference,1))):
        return sum
    else:
        return exp(1-len(ngram(candidate,1))/len(ngram(reference,1)))


def bleu(candidate, reference, n=1):
    if(len(reference)==0):
        return False;
    candidateList=ngram(candidate,n)
    referenceList=ngram(reference,n)
    cnt=NumOfIntersection(candidateList,referenceList)/ len(candidateList);
    return cnt

def ngram(str,n=1):
    '''
    返回一个字符串的ngram切分
    :param str:
    :param n:
    :return:list of str
    '''
    if len(str)<n:
        return []
    str=str.split(' ')
    string=""
    list=[]
    for i in range(len(str) - n + 1):
        for j in range(0, n):
            string += str[i + j]+" " if j<n else str[i + j]
        list.append(string)
        string=""
    return list;

def NumOfIntersection(candidate,reference):
    '''
    返回两个list的相同元素个数（不去重）
    :param candidate:
    :param reference:
    :return:int
    '''
    candidateCounter=dict(Counter(candidate))
    referenceCounter=dict(Counter(reference))
    cnt=0
    for key in candidateCounter.keys() &referenceCounter.keys():
        cnt+=min(candidateCounter[key],referenceCounter[key])
    return cnt;
print(bleu("the the the the", "the cat is standing on the ground", 1))